Method of taking a proportional sample of flowing gas in a line

ABSTRACT

Disclosed is a method for taking a constantly proportional flowing sample of gas flowing through a line and which is part of measuring and determining the total energy flow, that is, BTUs per minute, of combustible gas flowing through a line such as a pipeline. One method includes taking a continuous sample of the gas flowing through the line which sample is a constant proportion of the gas flowing through the line, and burning the sample in equipment which supplies air to the sample in an amount which maximizes its burning temperature. The flow rate of air which produces the maximum burning temperature of the sample is a flow rate which is directly proportional to the rate of energy flow in the main pipeline. Alternately, the flow rate of air which produces a stoichiometric mixture is directly proportional to the rate of energy flow in the main pipeline. Still further, if an excess of air is flowed to the flame, the amount of excess unconsumed oxygen is also a function of the rate of energy flow in the main pipeline. One or another of these parameters is measured.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation-in-part of application Ser. No. 071143,126, filedJan. 12, 1987, and now abandoned, which is a continuation-in-part ofapplication Ser. No. 033,919, filed Apr. 1, 1987, now abandoned, whichis a continuation of application Ser. No. 688,910, now abandoned, filedJan. 4, 1985, which is a continuation-in-part of application Ser. No.518,963 filed Aug. 1, 1983, now abandoned, which was a division ofapplication Ser. No. 272,204, filed June 10, 1981, now U.S. Pat. No.4,396,299, issued Aug. 2, 1983.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to measuring the total energy flow rate ofcombustible gas and, more particularly, to a method of taking a flowingsample which is proportioned to the total energy flow rate.

2. History of the Prior Art

The dollar value of BTUs contained in natural gas, and other combustiblegases, has increased the need to measure accurately the total energyflow rate of gas moving through pipe line systems, both at points nearthe point of use of the gas, and at points which may be remote from thepoint of use. The conventional methods for determining total energy flowrate at a point in a gas pipeline generally involve the simultaneous (orat least contemporaneous) measurement of several gas parameters whichare then employed as inputs into calculations ultimately producing avalue for energy flow. For example, one approach is to measure thepressure drop across an orifice plate in the line to obtain a startingpoint for calculation of flow rate, and to simultaneously measure thetemperature and pressure of the flowing gas and its composition at thetime (the latter being measured by a gas chromatograph). Thecomposition, pressure and temperature measurements provide the datanecessary for calculation of the density of the gas at the orificeplate. The calculated density and the before mentioned pressure dropacross the orifice plate provide the data necessary for calculation ofthe volumetric flow rate. The gas composition measurement, takentogether with the known heat of combustion values for various compoundsand elements, enables one to calculate the heat of combustion per unitvolume. Finally, the calculated heat of combustion per unit volume canbe multiplied by the calculated volumetric flow rate to give a value forenergy flow rate.

It can be seen that this approach and other similar conventionalapproaches which involve the making of multiple measurements of gasproperties or parameters suffer from the apparent disadvantage that eachmeasurement or type of measurement involves measurement errors. Theerrors of the multiple measurements accumulate and contribute an errorin the final calculated value, which error may be quite sizable. Inaddition, each measurement made on the gas involves a measuring entitycomprising some quality of equipment which must be maintained, andfurther involves periodic calibrating of that equipment to the desiredor best possible accuracy. Furthermore, such approaches, to the extentthat they involve hand calculations, also present opportunities forcalculation errors.

SUMMARY OF THE INVENTION

In accordance with the present invention, a method is provided formeasuring total energy flow rate of combustible gas flowing in a line.The method involves making only a single measurement of a parameterwhich stands in constant proportion to the total energy flow rate of themoving gas. The invention involves two basic steps: The first stepinvolves the taking of a continuous or flowing sample of the gas flowingin the pipeline, which sample is a constant fraction of the gas flowingthrough the line. The second step preferably involves burning of thesample with an amount of air which results in the combustion temperaturebeing maximized. When the burning occurs under conditions which maximizethe combustion temperature, then the air flow rate producing thatcondition is proportional to the energy flow in the gas flowing throughthe main pipeline. In a sense, the sample of combustible gas is"titrated" with air. The present invention, thus in part, makes use oftechniques disclosed and claimed in Clingman, U.S. Pat. No. 3,777,562issued Dec. 11, 1973; U.S. Pat. No. 4,062,236 issued Dec. 13, 1977; U.S.Pat. No. 4,125,018, issued Nov. 14, 1978; and U.S. Pat. No. 4,125,123also issued Nov. 14, 1978. Furthermore, the present invention preferablymakes use of a flow measurement system for determining air flow of thekind disclosed and claimed in Kennedy, U.S. Pat. No. 4,285,245, issuedAug. 27, 1981.

As is set forth hereinafter, the second step in the determination of thetotal energy flow rate of combustible gas flowing in a line mayalternately comprise forming a stoichiometric mixture of air and thesample of combustible gas and burning it. The rate of air flowsufficient to produce the stoichiometric mixture is also directlyproportional to the energy flow rate in the main pipeline. As a varianton this latter step, an excess of air may be flowed to the sample flame,and the residual oxygen flow in the exhaust gas measured. The level ofresidual oxygen flow is also a function of the energy flow rate in themain pipeline.

Since the present invention involves the making of only a singlemeasurement, it represents a material advance in the accuracy ofdetermination of total energy flow rate of gas moving through a line,because the stacking up or accmulation measurement errors inherent inmethods involving the measurement of multiple parameters are eliminated.

The taking of the proportionally constant sample in accordance with thepresent invention may be performed in any satisfactory manner. In somesituations, a simple branching of the main gas flow pipeline into a mainline and a sample line using conventional hardware may be adequate toprovide for the proportionally constant sampling. In most situations,however, such a simple arrangement of hardware will not suffice toprovide the uniformity of the proportional sampling desired.

Accordingly, it is preferred that the equipment for the continual takingof a proportionate sample of the gas flowing through the line inaccordance with the method of the invention includes an orifice plateflow meter in the main gas pipeline, a sample line tapped into the mainpipeline upstream from the orifice plate, an orifice plate in the sampleline, and equipment for adjusting the pressure downstream of bothorifice plates to the same value. The downstream pressure equalizingequipment may take any one of several forms as will be made clear in thediscussion of the detailed embodiments which follow.

As will be set forth hereinafter, a consideration of the orificeequations will reveal that when (a) the pressure drop across eachorifice plate is adjusted and maintained at a uniform level; (b) the gastemperature and composition at each orifice plate are uniform; and (c)the upstream pressures are uniform (all of which conditions being met inaccordance with the invention), the ratio of flow rates between the maingas flow pipeline and the sample line are in a fixed ratio, dependentprimarily on relative orifice area.

While it is possible to measure the pressure drops across the main lineand sample line orifice plates and to calculate from the pressure dropmeasurements the respective flow rates, this is not strictly necessaryfor the routine practice of the invention. What is of interest is not somuch the value of the flow rates as the circumstance that the sampleline gas flow rate is a constant proportion of the main line gas flowrate, assuming, of course, that the equipment has been properlycalibrated.

As mentioned above, the sample flowing through the sample line iscombusted or burned with air. In a preferred embodiment the flow rate ofthe air for combustion is measured. The air flow rate is varied oradjusted so that the combustion temperature is at a maximum. When thiscondition is met, the air flow rate is directly proportional to the flowrate of energy in the main pipeline. While the maximum temperaturemethod is presently preferred, the alternate methods involvingstoichiometric mixtures or deliberate excesses of combustion air mayalso be employed.

As a matter of equipment for carrying out the method of the invention,the several apparatuses shown in above mentioned U.S. Pat. Nos.4,125,123; 4,125,018, 4,062,236 and 3,777,562 may be used in variousembodiments, if suitably modified. In this connection, it should benoted that in said patents a number of the embodiments perform a flowrate measurement step on the gas stream rather than on the air stream,although in each case this procedure is a matter of choice. When suchequipment is used in the practice of the present invention, the flowrate measurement of the air stream is the measurement which is ofinterest and which is, as a practical matter, the stream which must bemeasured. Thus, persons with ordinary skill in the art will understandhow to modify or alter the equipment shown in the above listed patentsto accommodate it to the practice of the present invention.

It should also be noted that the air flow rate which produces a maximumadiabatic flame temperature is also, within very close limits, equal tothe air flow rate which produces a stoichiometric mixture with theparticular gas composition flowing through the main pipeline.

This circumstance leads to the alternate methods of performing thesecond step of the invention. Thus, starting with an excess of air, theair flow rate of the air may be slowly lowered and monitored by anoxygen detector in the exhaust gas from the flame where the sample isburned. When the oxygen detector indicates a sharp decrease in oxygen inthe exhaust gas, it is then known that the air flow rate is sufficientto produce a stoichiometric mixture. As another variant manner inperforming the second step, an excess of air may be flowed to combustwith the sample of combustible gas. The oxygen flow in the exhaust gasfrom the flame can be mentioned, and the level of excess flow or remnantair in the exhaust gas stream is a linear function of the energy flowrate in the sample stream and in the gas stream in the main pipeline.

From the foregoing it can be seen that the primary object of theinvention is a method and apparatus for accurately and convenientlymeasuring the total energy flow rate of a gaseous fuel moving through aline.

Another object of the invention is to provide a method and apparatus fortaking a continual sample of gas from a gas flowing through a main line,which sample is a constant proportion of the gas flowing through themain line.

Still another object of the present invention is to provide a method andapparatus for dividing a flow gas stream into constantly proportionatestreams.

Still another object of the present invention is to provide a method andapparatus whereby the energy flow rate in a gas flowing through a linemay be readily determined without resorting to a multiplicity ofmeasurements.

The manner in which the foregoing and other objects are attained,together with other objects and purposes of the invention, may best beunderstood by considering the detailed description which follows,together with the accompanying drawings.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic elevational view of a system constructed inaccordance with the invention and operating to practice the methodaspects of the invention;

FIG. 2 is a diagrammatic elevational view of proportionate samplegathering equipment of the system of FIG. 1;

FIG. 3 is a diagrammatic elevational view of an alternate type ofequipment for gathering proportionate samples in accordance with theinvention;

FIG. 4 is a diagrammatic elevational view of another alternate type ofequipment for gathering proportionate samples in accordance with theinvention;

FIG. 5 is a diagrammatic elevational view of yet another alternate typeof equipment for gathering proportionate samples in accordance with theinvention; and

FIG. 6 is a diagrammatic elevational view of another embodiment of theinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Attention is first directed to FIGS. 1 and 2 which illustrate a methodand equipment of the invention in one preferred form. In these figures amain gas pipeline is designated 10 and the flow of gas through thepipeline 10 from left to right is indicated by arrow 11. In the pipeline10 is mounted an orifice plate 12 having an orifice opening 13. Upstreamof the orifice plate 12 a branch line 14 is tapped into main line 10.The branch line 14 also has an orifice plate 15 mounted therein, and theorifice plate 15 has an orifice opening 16 The equipment described tothis point thus consists of the main pipeline 10 having the orificeplate 12 positioned therein, and the branch line 14 positioned therein.

FIGS. 1 and 2 are diagrammatic and the combination of the branch line 14and a branch line 18 (hereinafter described) is intended to representboth pipe taps and flange taps, it being understood that flange tapswould be located in flanges which would support orifice plate 12 in amanner well known in the art. Pipe taps would be inserted into pipeline10 essentially as illustrated in FIGS. 1 and 2.

For determining the rate of flow of a gas through the orifice 13 of theorifice plate 12, and the orifice 16 of the orifice plate 15, oneemploys the so-called "Hydraulic" equation, namely:

    Q.sub.s =KA√2gh                                     (Equation No. 1)

where

Q_(s) =Quantity rate of flow at the average specific weight ofmeasurement in cu ft per second

K=Coefficient of discharge including velocity of approach factorcorresponding to the condition of measurement

A=Area of orifice in sq ft

g=Acceleration due to gravity in ft per second per second

h=Differential head in feet of the fluid flowing and at the averagespecific weight at the orifice

EQUATIONS FOR USE IN GAS MEASUREMENTS

In the measurement of most gases, the generally accepted practice is toexpress the flow in cubic feet per hour to a specific reference or basecondition of pressure and temperature. The differential head is measuredin inches of water, and the static pressure in lbs. per sq. in. Theabove-identified Hydraulic equation (Equation No. 1) can thus bearranged to give results directly in these units by substituting in thenecessary values. It will then read

    Q.sub.h =C'√h.sub.w p.sub.f                         (Equation No. 2)

where

Q_(h) =Quantity rate of flow at base conditions in cu ft/hr

h_(w) =Differential pressure in inches of water

p_(f) =Absolute static pressure, psia

C'=Orifice flow constant (this corresponds to what was formerly calledthe hourly coefficient) which is found by substituting the followingvalues in Equation 1

    g=32.17 ##EQU1## γw=62.37 specific weight of water at 60° F. in lb/cu ft γ=Actual specific weight of gas at flowing conditions in lb cu/ft ##EQU2##  where d=Orifice diameter in inches, and

Qf=3600 Qs=Quantity rate of flow at flowing condition in cu ft/hr

If one then takes the specific weight of dry air at 14.70 psia and 32°F. to be 0.08073 lb/cu ft then Boyle's and Charles' laws for gases willgive ##EQU3## where T_(f) =Absolute flowing temperature in degreesRankine, which is obtained by adding 460 to the flowing temperature indegrees Fahrenheit

G=Specific gravity of the flowing gas, dry air=1.000

Tb=Absolute temperature at reference or base condition, °R

Substituting the value of Q_(f) from Equation No. 7 in Equation No. 9gives ##EQU6## which may also be written ##EQU7## and, therefore,##EQU8##

COEFFICIENTS OF DISCHARGE

In both the Equation Nos 1 and 12, a discharge coefficient K appears.This has to be determined experimentally and is known in the art. Thetests have shown that for any one type of pressure taps, K varies withD, the size of the pipe; d, the size of the orifice; Q_(s), the rate offlow through the orifice; , specific and the viscosity of the fluidflowing. If the fluid is a gas, this coefficient also varies with x, theratio of differential to upstream pressure; and k, the ratio of specificheats of the gas.

In order to predict accurately what the coefficient of any orifice isgoing to be, all of the above mentioned facts concerning the flowingfluid must be known. The relations between these functions can besomewhat simplified for application to commercial use and thecoefficient shown to depend on the Reynolds number, acoustic ratio, pipesize, and orifice diameter ratio. The Reynolds number is a dimensionlessratio and is expressed as ##EQU9## The acoustic ratio is expressed as##EQU10## where ##EQU11## the ratio of differential pressure to absoluteinlet static pressure where

p_(f1) =Absolute static pressure at upstream pressure tap, psi

p_(f2) =Absolute static pressure at downstream pressure tap, psi

and ##EQU12## the ratio of specific heat of the gas at constant pressureto specific heat of the gas at constant volume

The orifice diameter ratio is expressed as ##EQU13## where D=The actualinternal pipe diameter in inches

EMPIRICAL EQUATIONS FOR K

The values of K used in the flow equations can be calculated byempirical equations derived from tests.

These empirical equations may be written as follows ##EQU14## In theabove equations ##EQU15## For either pair of taps ##EQU16## where K_(o)=The coefficient of discharge for infinite Reynolds number which will bethe minimum value for any particular orifice and pipe size.

The value of E is given by the following

    E=d(830-5000β+900β.sup.2 -4200β.sup.3 +B) (Equation No. 18)

where ##EQU17##

Thus K for any value of Rd can be calculated using the followingequation ##EQU18##

The coefficients calculated from these equations apply to orifices,provided the pipe is not less than 1.6 inches inside diameter and thediameter ratio is between 0.10 and 0.75. Under these conditionscoefficients calculated for Flange Taps by the above equations aresubject to a tolerance of plus or minus 0.5% when the diameter ratio isbetween 15% and 70%. When the diameter ratio is less that 15% or greaterthan 70%, the tolerance is to be increased to plus or minus 1%. For PipeTaps, the tolerance is plus or minus 0.75% for diameter ratios between20% and 67%, and may be as high as plus or minus 1.5% for diameterratios below 20% or above 67%.

ORIFICE FLOW CONSTANT, C'

To compute K and then C' for each meter by the direct these empiricalequations would be too time-consuming for routine work; hence somesimplification is necessary. A convenient way of making this computationis to write another equation for the orifice flow constant C', namely,

    C'=F.sub.b F.sub.γ Y F.sub.pb F.sub.tb F.sub.tf F.sub.g F.sub.pv F.sub.m F.sub.a F.sub.1                                   (Equation No. 22)

in which

F_(b) =Basic orifice factor

F.sub.γ =Reynolds number factor

Y=Expansion factor

F_(pb) =Pressure base factor

F_(tb) =Temperature base factor

F_(tf) =Flowing temperature factor

F_(g) =Specific gravity factor

F_(pv) =Supercompressibility factor

F_(m) =Manometer factor

F_(a) =Orifice thermal expansion factor

F₁ =Gage location factor

BASIC ORIFICE FLOW FACTOR, F_(b)

The basic orifice flow factor may be defined by the equation ##EQU19##

This is not the same as Equation No. 12 because K_(o) is the particularvalue of K when R_(d) =.

By using the values:

T_(b) =T_(f) =520° R p_(b) =14.73 psia and G=1.000

Equation No. 23 reduces to

    F.sub.b =338.17d.sup.2 K.sub.o                             (Equation No. 24)

Now K_(o) may be calculated from Equation Nos. 15, 17, 18, and 19 forFlange Taps, and from Equation Nos. 16, 17, 18 and 20, for Pipe Taps,and tables prepared for values of F_(b) (Flange) and F_(b) (Pipe) forvarious values of D and d. The steps in the values of D and d may be sospaced as to make possible linear interpolation of intermediate values.

REYNOLDS NUMBER FACTOR, Fγ

The Reynolds number factor F is introduced because in any actual case ofmetering the Reynolds number R_(d) will have a finite value; hence thecorresponding value of K will be somewhat greater than K_(o). FromEquation No. 21 one has as a definition. ##EQU20##

E can be calculated from Equation Nos. 18 and 19 for Flange Taps andEquation Nos. 18 and 20 for Pipe Taps. The value of the Reynolds numberas given in Equation No. 13, is thus ##EQU21##

V_(f) can be calculated from an equation similar to Equation No. 7,since ##EQU22## then ##EQU23##

However, before V_(f) can be calculated, it is necessary that the valueof K be known or assumed. A study of the variation in the value of Kwith changes in pipe sizes and Reynolds number over the range ordinarilyencountered in the measurement of natural gas showed that for anyselected values of β, this variation is within plus or minus 2%. If anaverage value of K were used for any diameter ratio this 2% variation inK would cause a maximum variation of only about 0.05% in the values ofFγ. Tables are known giving these average values of K for Flange andPipe Taps used for the calculation of V_(f) in order to determineF.sub.γ. Linear interpolation should be used for determiningintermediate values of K to be used in calculating R_(d) by Equation No.28.

A series of determinations of the viscosity of natural gas, made by theU.S. Bureau of Mines, and a survey of the composition of the gasesmeasured with orifice meters in representative locations throughout thecountry, indicated that μ=0.0000069 lb/ft-sec is a fair average value.Using this value of μ, and assuming T_(f) =520° R, and G=0.65, we havefrom Equation Nos. 13 and 27. ##EQU24##

By combining Equation Nos. 25 and 28, ##EQU25## To compute the values ofF, a series of values of b are computed for the several orificediameters d with a given line size D. Values of K are available fromknown tables for these various ratios of d/D. Values of E are computedfor the same values of d and D.

Equation No. 31 is suitable for use with natural gases having certaincharacteristics. When gases with other characteristics are to bemeasured Equation No. 31 should be adjusted as follows: ##EQU26## whenviscosity is expressed as ##EQU27##

EXPANSION FACTOR, Y

When a gas flows through an orifice, the change in velocity and pressureis accompanied by a change in specific weight and a factor must beapplied to the coefficient to allow for this change. This factor isknown as the "Expansion Factor Y" and can be calculated from thefollowing equations: ##EQU28## where k=Ratio of specific heats.##EQU29## Y₁ =The expansion factor based on the upstream absolutepressure. The values of Y₁ computed by these equations are subject to atolerance varying from 0 when x=0, to plus or minus 0.5% when x=0.20.For larger values of x, a somewhat larger tolerance may be expected. Theequation for Flange Taps may be used for a range of diameter ratios from10% to 80%, while that for Pipe Taps may be used over a range from 10%to 70%.

If the static pressure is taken at the downstream pressure tap then thevalue of the expansion factor Y₂ can be calculated using the equation##EQU30##

In some cases the mean static pressure between upstream and downstreampressures is more useful, and if this is used, the expansion factorY_(m) can be calculated by ##EQU31##

Natural gases are generally assigned a specific heat ratio k of 1.3.When the gases being measured have significantly different k values thedesirability of using adjusted Y values can be determined as follows:

Adjusted value of ##EQU32## where Y₁ =value read from known Tables, suchas Tables 6 and 10 of "Orific Metering of Natural Gas", AGA Report No.3, 1978, American Gas Association, Arlington, VA; and

K=specific heat ratio for gas in equation.

Adjusted value of ##EQU33## Wherein Y₁ and Y₂ are obtained from Tablessetforth in "Orifice Metering of Natural Gas" (Supra).

PRESSURE BASE FACTOR, F_(pb)

The pressure base factor F_(pb) is applied to change the base pressurefrom 14.73 psia, and is calculated by dividing 14.73 by the required(contract) absolute base pressure. The use of this factor is equivalentto substituting the (contract) absolute base pressure in Equation No. 23in place of 14.73. ##EQU34## where p_(b) =The required contract basepressure, psia

TEMPERATURE BASE FACTOR, F_(tb)

The temperature base Factor F_(tb) is applied where the base temperatureis other than 60° F. and is calculated by dividing the required(contract) base temperature in degrees Rankine by 520°. The use of thisfactor is equivalent to substituting the contract absolute temperaturebase instead of 520° R in Equation No. 23 ##EQU35## where T_(b) =Therequired (contract) base temperature in degrees Rankine.

FLOWING TEMPERATURE FACTOR, F_(tf)

The flowing temperature factor F_(tf) is required to change from theassumed flowing temperature of 60° F. to the actual flowing temperatureT_(f) and is determined by dividing 520° by the flowing temperature indegrees Rankine and taking the square root of the results. The use ofthis factor is equivalent to substituting the actual absolute flowingtemperature in place of the assumed temperature of 520° R in EquationNo. 23. ##EQU36## where T_(f) =Actual flowing temperature of the gas indegrees Rankine.

SPECIFIC GRAVITY FACTOR, F_(g)

The specific gravity factor F_(g) is to be applied to change from aspecific gravity of 1.0 to the real specific gravity of the flowing gas,and is obtained by taking the square root of 1 divided by the realspecific gravity. The use of this factor is equivalent to substitutingthe real gravity for the assumed value of 1 in Equation No. 23.##EQU37## Almost universally the specific gravities used by the industryhave been determined by relative density measurement made with gravitybalances. The procedures have only required that the observations beadjusted so both the air and gas measurements reflected the samepressure and temperature. The fact that the temperature and pressureswere not tied down has resulted in small variances in specific gravitydeterminations. Another small source of variance has been thatatmospheric air has been used and its composition (also molecular weightand density) varies from place to place and time to time at any givenlocation.

Where recording gravitometers are used and calibration is performed withreference gases, either "ideal" or "real" specific gravity can beobtained as the recorded specific gravity simply by the propercertification of the reference gas.

The relationship of the defined IDEAL SPECIFIC GRAVITY AND REAL SPECIFICGRAVITY is established as follows: ##EQU38##

SUPERCOMPRESSIBILITY FACTOR, F_(pv)

Boyle's law for gases states that the specific weight of a gas isdirectly proportional to the absolute pressure, the temperatureremaining constant. All gases deviate from this law by varying amounts,and with the range of conditions ordinarily encountered in the naturalgas industry the actual specific weight under the higher pressures isusually greater than the theoretical. When this deviation is representedby Factor Z, as above, and is applied to the evelopment of the orificemeter flow formula an expression including the factor √1/Z results. Forconvenience, this factor is termed the Supercompressibility Factor anddesignated as Fpv.

The method of supercompressibility factor evaluation bases the directfactor determination on the relating of the compressibility variation ofvarious natural gases to that of a 0.600 specific gravity hydrocarbongas.

Normal mixtures are defined as mixtures of essentially methane andethane plus heavier hydrocarbon components, but not containingappreciable concentration of the much heavier natural gas hydrocarbons.The diluent content of any gas mixture to which the method is to beapplied should be limited to 15 mol per cent carbon dioxide and 15 molper cent nitrogen and actual tests are recommended for diluent contentexceeding these quantities.

The specific gravity, carbon dioxide and nitrogen contents, inconjunction with the flowing pressure and temperature is used todetermine the adjusted pressure and temperature necessary for relatingany gas to the supercompressibility data of the 0.600 specific gravity,hydrocarbon gas.

Specific Gravity Method of Supercompressibility Factor Determination(A.G.A. Standard Method):

The adjusted pressure is obtained by multiplying the gage pressure ofthe flowing gas by the pressure adjusting factor F_(p) and the adjustedtemperature is obtained by multiplying the absolute temperature of theflowing gas by the temperature adjusting factor F_(T) and subtracting460 from this product. Adjusting factors F_(p) and F_(T) are calculatedas follows: ##EQU39## where

    Kp=Mc-0.392Mn                                              (Equation No. 43)

and ##EQU40## where

    KT=Mc+1.681Mn                                              (Equation No. 45)

and

G=Specific gravity of flowing gas

Mc=Mol percent carbon dioxide

Mn=Mol percent nitrogen

    Adjusted Pressure=P.sub.f F.sub.p psig                     (Equation No. 46)

    Adjusted Temperature=T.sub.f F.sub.T -460° F.       (Equation No. 47)

After the adjusted pressure and the adjusted temperature are determinedthe supercompressibility factor F_(pv) can be determined from availabledata,such as Table 16 in "Orific Metering of Natural Gas" (supra).

MANOMETER FACTOR, F_(m), and LOCATION FACTOR, F¹

The manometer and location of factors are introduced to correct for theerror in differential pressure indication in mercury manometer typegages caused by: (1) the weight of the gas column above the mercury; (2)the change in the specific weight of the mercury at temperatures otherthan the base temperature of 60° F.; and (3) the change in the specificweight of the mercury when subjected to gravitational forces departingfrom the international standard given for sea-level elevation at exactly45° geographic latitude, i.e. 980.665 cm/sec/sec.

The basic equations for the combined manometer and factors location are:

Gas column weight correction=[(γm-γg)/γ_(m) ]⁰.5

Mercury column temperature correction=(γm/γm60)⁰.5

Mercury column gravitation correction=(g¹ /g^(s))0.5

Combined correction, ##EQU41## where g=Specific weight of gas displacingmercury, determined for the molecular weight of the gas at ambienttemperature and static pressure psia at the gage.

m=Specific weight of the mercury at ambient temperature and standardgravity.

m60=Specific weigh of mercury at base temperature of 60° F. and standardgravity (0.489771 lb/in.³).

g1=Local gravity, cm/sec²

g_(s) =Standard gravity at sea level, 45° latitude (980.665)

It will be noted g1 values are constants for any given measuringlocation, whereas other parameters to manometer factor selection arevariables. Thus, in practice, the equation is best rewritten to isolatevariables from constants. ##EQU42## By substituting the density ofmercury per cubic foot (0.489771 lb/in.³ ×1728=846.324) at basetemperature of 60° F. and standard gravity of 980.665 cm/sec², themanometer factor equation resolves to: ##EQU43##γm=846.324×[1-0.000101(T_(a) -520)] By susbtituting the standard gravityat sea level, 45° latitude (980.665 cm/sec²) in equation No. 49b##EQU44## The ambient value of gravity at any location is mostaccurately obtained from U.S. Coast and Geodetic Survey data, referenceto aeronautical data or from Smithsonian Meteorological Tables. In theabsence of better data, practical values of g1 may be obtained byequation over the midlatitudes, between 30° and 60°.

g1=980.665+[0.087(° L -45)]-0.000094H

A curve fit equation covering latitudes from 0° to 90° may also be used:

g1=978.01855-0.0028247L+0.0020299L² -0.000015085L³ -0.000094H

where

°L=Degrees latitude

H=elevation in lineal feet above sea level

Other equations relating local gravity to latitude may be obtained fromsuch sources as N.B.S. Nomograph 8.

ORIFICE THERMAL EXPANSION FACTOR, F_(a)

The Orifice Thermal Expansion Factor is introduced to correct for theerror resulting from expansion or contraction of the orifice operatingat temperatures appreciably different from the temperature at which theorifice was bored. The factor may be calculated from the followingequation:

304 and 316 stainless steel

    F.sub.a =1+[0.0000185(°F. -68)]                     (Equation No. 52)

Monel

    F.sub.a =1+[0.000159(°F. -68)]

    °F.=gas flowing temperature at orifice              (Equation No. 53)

These formulas assume the orifice bore diameter, d, has been measured ata temperature of 68° F.

MEASUREMENT WHEN SPECIFIC WEIGHT IS KNOWN

In Equation No. 11, T_(f) and pf have been introduced in an attempt tocalculate γ, the specific weight of the gas at flowing conditions. Theinaccuracy of Boyle's and Charles' laws, when applied to natural gas athigh pressure, makes necessary the additional factor, F_(pv).

Equation No. 5 may be reduced to the form ##EQU45## Substituting for##EQU46## where:

K=K_(o) Fγ ##EQU47## T_(b) =520F_(tb) ##EQU48## Substituting theequivalent values in Equation No. 10a and inserting the expansion factorY to make the equation complete for compressible fluids, ##EQU49## Ifone lets ##EQU50## then

    Q.sub.h =C"√h.sub.w γ                         (Equation No. 2a)

MEASUREMENT IN WEIGHT UNITS

In certain industrial gas measurements, it may be desirable to measuregas in pounds. In that case, if the specific weight of the gas atflowing conditions is known, the formula for measurement becomes quitesimple, since the rate of flow in pounds per hour equals the rate offlow in cubic feet at flowing conditions times the specific weight atflowing conditions in pounds per cubic foot, i.e., W_(h) -Q_(f).

Substituting the value of Q_(f) from Equation No. 7, ##EQU51## FromEquation No. 5, ##EQU52## Substituting in Equation No. 7b, ##EQU53##Since, from previous equations ##EQU54## Substituting the equivalentvalues in Equation No. 10b and inserting the expansion factor Y to makethe equation complete for compressible fluids, ##EQU55## If we letC'"=1.0618F_(b) Fr^(Y) W_(h) =C'"√h_(w) γ

Factors such as F_(m), F₁ and F_(a) should be applied in weight flowmeasurements where applicable.

Thus, using the foregoing equations one can determine the gas flowthrough the orifice opening 13 of the orifice plate 12 and the orificeopening 16 of the orifice plate 15. Further, the subscripts set forth inthe formulas, namely, 12 and 15, represent the orifice opening 13 and 16of the orifice plates 12 and 15, respectively.

The equations for gas flow through orifices 13 and 16 of the orificeplates 12, 15, respectively, are as follows:

1) Q₁₂ =K₁₂ A₁₂ (2gh₁₂)1/2

2) Q₁₅ =K₁₅ A₁₅ (2gh₁₅)1/2

Q=Rate of flow in cubic feet per second.

K=coefficient of discharge

A=orifice area

g=acceleration due to gravity

h=differential head across orifice

As previously stated, the subscripts 12 and 15 associates with theparameters defined immediately preceding in the above equations and theequations hereinafter set forth refer to the orifice opening 13 and 16and the orifice plates 12 and 15, respectively and thus define therespective equations for each orifice plate. Further, the followingequations are derived in the same manner as the before-describedequations and explanations thereof as set forth in "Orific Metering ofNatural Gas", AGA Report No. 3, 1978, American Gas Association,Arlington, Va.

Because of the metal structure the temperature at both of the orificeplates 12 and 15 will be the same. The gas composition is the same inboth cases. The pressures on both sides of orifice 13 are also the sameas the corresponding pressures across orifice 16. Thus, the gasproperties on both sides of the orifice plates 12 and 15 are identicalin the two cases. The ratio of the two flows is then given by Q₁₅ /Q₁₂.Further, since the acceleration due to gravity (i.e., g is the same forboth the orifice plates 12 and 15,) and the differential head across theorifices 13 and 16 are equal, Q₁₅ /Q₁₂ is represented by the followingequation:

    Q.sub.15 /Q.sub.12 =(A.sub.15 /A.sub.12)(K.sub.15 /K.sub.12)

The general equation for the discharge coefficient is ##EQU56## whereK_(i) the coefficient of discharge for infinite Reynolds number whichwill be the minimum value for any particular orifice and pipe size j andK_(i) =Coefficient of discharge when the Reynolds number is equal to##EQU57## Solving the above equations one determines that: K_(i) =K_(i)'(1+E_(i) /R_(di))

i=orifice reference number ##EQU58## R_(di) =Reynolds number=V_(i) d_(i)p/μ d_(i) =orifice diameter

V_(i) =jet velocity in the plane of the orifice

ρ=gas density

μ=viscosity.

E_(i) is known to be defined as hereinbelow set forth.

Applying this equation to orifices 13 and 16 of orifice plates 12, 15,respectively, gives:

K₁₂ =K₁₂ ' (1+E₁₂ /R_(d12))

and

K₁₅ =K₁₅ ' (1+E₁₅ /R_(d12)).

E_(i) in the equation for discharge coefficient is defined as follows:

4) E_(i) =d_(i) (830-5000b_(i) +9000b_(i) ² -4200b_(i) ³ +B_(i))

D_(i) =pipe diameter

b_(i) =d_(i) /D_(i)

where B_(i) =530/D_(i) ^(1/2) for flange taps

and

B_(i) =(875/D_(i))+75 for pipe taps

The effective area of the jet in the plane of the orifice is A_(i)K_(i).

Thus,

V_(i) =Q_(i) /A_(i) K_(i)

It thus follows that V₁₂ =V₁₅ and R_(d12) /^(d) 12=R_(d15) /^(d) 15.

Now define the function F(b) as follows:

F(b_(i))=(E_(i) /d_(i)) -B_(i)

Using the above equations the data tabulated below was calculated.

    ______________________________________                                                 b   F(b)                                                             ______________________________________                                                 .7  299                                                                       .6  163                                                                       .5   55                                                                       .4   1                                                                        .3   27                                                                       .2  156                                                                       .1  416                                                              ______________________________________                                    

The design equations for orifice 16 are now as follows:

FLANGE TAPS: F(b₁₅)+530/(D₁₅)1/2=F(b₁₂)+530/(D₁₂)1/2

PIPE TAPS: F(b₁₅)=875/D₁₅ =F(b₁₂)+875/D₁₂

b₁₅ and D₁₅ are chosen so as to minimize the flow through line 14 and tosatisfy these equations.

Downstream from the orifice plates 12 and 15 respectively, main line 10and branch line 14 are connected by pressure equalizing means designatedgenerally as 17. In the embodiment of FIGS. 1 and 2 this means includesa line 18 interconnected between the main pipe line 10 and branch lineor sample line 14. A piston 19 is positioned to move within the line 18.Microswitch points 20 and 21 are positioned in line 18 to be connectedby piston 19 when it is in the line 18 in the immediate vicinity of themicroswitch points 20 and 21. Downstream in line 14 from the point ofinterception of line 18 with line 14 there is mounted motorized valve22.

The operation of the equipment described to this point is as follows:

Assuming that motorized valve 22 is closed, the situation will be thatthe upstream pressure on orifice plates 12 and 15 will be equal, but thedownstream pressure will be unequal. It will be lower in the main line10 than in branch line 14. In branch line 14 the pressure on thedownstream side of orifice plate 15 will b substantially equal to theupstream pressure by reason of the closed condition of valve 22. Underthese circumstances piston 19 will move towards microswitch point 20 andwill make the circuit through microswitch point 20. This event actuatesmotorized valve 22 to open and it will eventually open sufficiently sothat the pressure on the downstream side of the orifice plate 15 will belower than that on the downstream side of the orifice plate 12 in mainline 10. These conditions will cause piston 19 to move towardsmicroswitch points 21, and upon closing the circuits through themicroswitch points 21, will actuate motorized valve 22 to close. Uponclosure of the valve 22 the first described set of conditions in theoperations will exist once again. The piston 19 thus migrates back andforth between microswitch points 20 and 21 for alternately opening andclosing the motorized valve 22. Thus, on the average, the pressuredownstream of orifice plate 12 and orifice plate 15 is equal, eventhough at any particular moment the downstream pressures may in fact beunequal.

Attention is now directed to FIG. 3 which shows another set of equipmentfor accomplishing a division of the gas stream into that flowing in themain pipe line and the proportionate fraction flowing in the branch line14. In FIG. 3 the same reference characters are used for substantiallyidentical parts

The embodiment of FIG. 3 a differential pressure guage or meter 23 isinterposed in line 18 to compare the downstream pressure in main pipeline 10 and branch line 14. A comparison signal is sent to amicroprocessor controller 24 where it is conventionally processed tosend a signal to motor 25 of motor driven valve 26 to open or close thevalve 26 in a manner to bring the two downstream pressures to equality.

In FIG. 4 there is illustrated still another set of equipment forperforming the proportionate sample taking function. In the embodimentof FIG. 4 there is interposed in line 18 a housing 27 having a diaphragm28 connected across the interior thereof. A follower 29 is connected tothe diaphragm 28 and passes through an opening in the wall of housing27. The follower 29 carries a wiper working on the slide wire of apotentiometer associated with a control box 30 which generates a signalwhich is addressed to a motor 31 of a motor controlled valve 32. Whenthere is an imbalance in downstream pressures in lines 10 and 14 thediaphragm 28 will be moved upwardly or downwardly and its follower 29will move to a different point on the slide wire of controller 30.

Attention is now directed to FIG. 5 which illustrates still anothermeans for establishing the pressure downstream of orifices 13 and 16 atthe same level. A diaphragm housing 60 is provided surrounding aflexible diaphragm 61. The lower side of the housing 60 is connected bya line 62 to the main pipeline 10 at a point downstream from the orifice13. The upper side of the housing 60 is connected by a line 63 to line14 at a point downstream of the orifice 16. Thus, the diaphragm 61 is inpressure communication with the two pressures of interest, those justdownstream of the orifice plates 12 and 15. The position of thediaphragm 61 with the housing 60 is thus a function of the twodownstream pressures.

A control rod 64 is connected to the diaphragm 61 and passes through anopening in the housing 60 and into a valve 65 provided in line 14. Thecontrol rod 64 carries valve plates 66, 67, which are seatable in valveopenings 68, 69, respectively, in a valve body 70.

In operation, if the downstream pressure in main line 10 is greater thanthat in line 14, the diaphragm 61 tends to close the valve 65 andincrease the pressure in the line 14. If the downstream pressure in theline 14 is greater, the diaphragm 61 tends to open the valve 65 toreduce that pressure. Thus the two pressures of interest tend to beequalized.

Returning now to FIG. 1 it can be seen that downstream of the motorizedvalve 22 in line 14 there is provided a ballast or surge tank 33. Thepurpose of the ballast tank 33 is to smooth irregularities in flowresulting from excursions of the piston 19 in the line 18. The size ofthe ballast tank 33 need only be relatively large compared to the volumeof the line 18 lying between the microswitch points 20 and 21. Ifequipment such as that shown in FIGS. 3 and 4 is employed in the sampletaking and establishing equipment, the surges in flow are likely to besmaller than that involved in the equipment of FIG. 1, and it may thusbe possible to dispense with the ballast tank 33 or to use a smallertank.

The flowing gas sample is led from the ballast tank 33 through a line 34to branch lines 35 and 36 where it is divided into two streams fordelivery to two burners 39 and 40. A capillary 37 is in line 35 and asimilar capillary 38 is in line 36.

Air is also delivered to the burners 39 and 40 through a speciallydesigned flow-control system of the kind disclosed in above mentionedU.S. Pat. No. 4,285,245. Air enters the system through a line 41 andpasses through a flow control and measurement system 42. A majorcomponent of the system 42 is a motorized valve 56. The air then passesinto a chamber 43 where its pressure is sensed by a transducer 44.Flowing air leaving the chamber 43 passes through a pressure regulator46 and a capillary 47 into line 48. Line 48 is divided into lines 49 and50 which lead to the burners 39 and 40, respectively. A capillary 51 isprovided in the line 49 and a capillary 52 is provided in the line 50.Between line 48 and capillary 51 is a valve 84. Between line 50 andcapillary 52 is a valve 85.

The rate of flow of energy into the flames of the burners 39 and 40,when their average temperature is at a maximum, is in direct proportionto the rate of air flow to the burners 39 and 40. This is an alternateway of stating the principal underlying the equipment just described andthe equipment for determining the calorific value of a fuel gasdescribed and shown in the above listed patents. In effect, in theequipment shown in FIG. 1, the fuel flow to the burners 39 and 40 is"titrated" with air, using the maximum flame temperature as detected bythermocouples 53 and 54 to determine the end point. The measured rate ofair flow is then in proportion to the rate of energy flow of the gasflowing in the conduit 14, and because of the proportionality of thatgas flow rate to the gas flow rate in the main pipeline 10, the air flowrate as measured is also in constant proportion to the energy flow ratein main pipeline 10.

The detected thermocouple signals from thermocouples 53 and 54 aredelivered to microcomputer 55 which processes the thermocouple signalsand sends appropriate derivative signals to control system 45 of theflowmeter. In response to the signals it receives, the control systemvaries the setting of the pressure regulator 46 to increase or decreasethe air flow to traverse it across the range of flow which produces adetectable maximum average temperature at the thermocouples 53 and 54.The motorized valve 56 is closed periodically by the control system andthe pressure fall in the chamber 43 is detected by the pressuretransducer 44 to provide a reading of the air flow rate, since the slopeof the time decay of pressure in the capillary 47 is proportional toflow rate, as is explained in greater detail in U.S Pat. No. 4,285,245.

In accordance with the invention other forms of flow measuring equipmentmay be employed for measuring the air flow rate. These alternate formsof air flow measurement include hot wire flowmeters, orifice plateflowmeters, rotometers, displacement meters of various sorts, and thelike.

Instead of monitoring the flame temperature to establish a flow rateproducing a maximum flame temperature, the oxygen flow, or lack thereof,in the exhaust immediately downtream from a burner may be monitored.Zirconium dioxide oxygen detectors are suitable for this purpose. Whenoxygen content in the exhaust gas is the detected parameter, only asingle burner is employed, and the gas and air flow to the other burnerin a unit may be terminated by suitable valves. In one embodimentemploying exhaust gas oxygen monitoring, the desired end point is asharp decrease in oxygen content in the exhaust gas, which means the airflow rate is producing a stoichiometric mixture. In another form of theinvention in which oxygen flow in the exhaust gas is measured, the airflow rate is established at a rate in excess of the stoichiometricamount, and the residual, remnant or excess oxygen flow in the exhaustgas is monitored to yield a parameter which is a known or calculatablefunction of the total energy flow rate in the main pipeline.

Returning now in FIG. 1, the equipment thereof for practicing theinvention in accordance with the two alternate modes just discussed maybe pointed out. In the exhaust gas lines above the burners 39 and 40 aremounted zirconium dioxide oxygen detectors 80 and 81, which are deviceswhose electrical output essentially switches from "on" to "off" when thestoichiometric point of oxygen content is crossed from rich to lean,thus providing a clear signal for that point. Also mounted in theexhaust lines are flowmeters 82 and 83, indicated diagrammatically asorifice plates in FIG. 1, although various sorts of flowmeters may beused. The flowmeters, in conjunction with the oxygen detectors, providethe data necessary for determining oxygen flow in the excess oxygen modeof operation.

Attention is now directed to FIG. 6 which illustrates another embodimentof the invention. In FIG. 6, a main pipeline is designated 100, while abranch or sample line is designated 101. An orifice plate 102 is mountedin the main line 100, and an orifice plate 103 in the sample line 101.The pressures downstream of orifice plates 102 and 103 are detected by adifferential pressure sensor 104. The output signal from sensor 104 isamplified and employed to control a motorized valve 105 to adjust thegas flow to equalize the downstream main line and sample line pressures.Sample line 101 also contains a regulator valve 106, and a flowmeter 107of suitable type, indicated diagrammatically as a box Fg. The outputsignals from the flowmeter 107 are delivered to a control computer 108,indicated diagrammatically as a box C.

An air line 109 is provided with a flowmeter 110, indicateddiagrammatically as Box Fa, installed therein. Signals from theflowmeter 110 are delivered to the computer 108. The air line 109 andthe sample line 101 join at 111 to deliver a combustible mixture througha line 112 to a burner 113. A detector 114 is positioned in or adjacentthe flame to detect maximum temperature (if a thermocouple) orstoichiometric point (if a zirconium dioxide detector). The signal fromthe detector 114 is amplified and employed to control a motorized valve115 to adjust the air flow to the desired end point.

In operation, the gas flow rate reported by the flowmeter 107 (Fg) isproportional to volume flow in the pipeline 100; and the air flow ratereported by flowmeter 110 (Fa) is proportional to energy flow rate inthe pipeline 100. The ratio of the air flow rate to the gas flow rate(Fa/Fg) is proportional to heat content per standard unit of volume. Thecomputer 108 may be programmed to compute this ratio, as well as applyproportionality constants to place the data Fg, Fa, and Fa/Fg in thedesired units.

In addition to providing a continuous measurement of energy flow in thepipeline, parts of the system can be used to measure volumetric flow inthe pipeline. This can be done much more accurately with this inventionthan with state of the art methods. The output from conduit 14 (SeeFIG. 1) can be measured at ambient pressure with a volumetricdisplacement meter. With the correct proportionality constant thisoutput can then give the integrated volume flow through the mainpipeline 10 measured at standard conditions. A time derivative of thisvolume will give the flow rate. Such a determination of flow rate wouldbe independent of gas properties and would require the measurement ofonly one parameter instead of several.

What is claimed is:
 1. A method of taking a flowing sample of gasflowing through a line, which flowing sample is constantly proportionateto the flow rate of said flowing gas, said method comprising:a) passingsaid gas flowing through said line through a first flow restriction insaid line; b) drawing a flowing sample of said gas from said line at apoint upstream of said first flow restriction into a sample line; c)passing said flowing sample of said gas in said sample line through asecond flow restriction in said sample line, the interior of said line,said first flow restriction, said sample line, and said second flowrestriction each being substantially cylindrical, the interior diameterof each of said four elements above being sequentially identified by thefollowing symbols: D₁₅, d₁₅, D₁₂, and d₁₂ ; d) equalizing the pressuredownstream of said first and second restrictions; and e) said first andsaid second flow restrictions being so sized with respect to each otherand said line and sample line that the equationF(b₁₅)+530√in/(D₁₅)^(1/2) =F(b₁₂)+530√in/(D₁₂)^(1/2) is true in the caseof flange taps adjacent said restrictions when D₁₂ and D₁₅ are expressedin the same units of measurement and the equation F(b₁₅)+875in/(D₁₅)=F(b₁₂)+875 in/D₁₂ is true in the case of pipe taps adjacentsaid restrictions when D₁₂ and D₁₅ are expressed in the same units ofmeasurement, b₁₅ is a parameter of said second flow equal to thedimensionsless quotient produced by having d₁₅ divided by D₁₅, b₁₂ isequal to the dimensionless quotient produced by having d₁₂ divided byD₁₂, F(b₁₅)=d₁₅ (830 per inch-5,000 per inch b₁₅ +9,000 per inch b₁₅ ²-4200 per inch b₁₅ ³ +B₁₅) wherein ##EQU59## for flange taps ##EQU60##for pipe taps, and F(b₁₂)=d₁₂ (830 per inch-5000 per inch b₁₂ +9000 perinch b₁₂ ² -4200 per inch b₁₂ ³ +b₁₂) wherein B₁₂ = ##EQU61## for flangetaps ##EQU62## for flange taps.
 2. A method in accordance with claim 1in which said equalizing of downstream pressures is achieved bydetecting the difference between said pressures and operating a valve insaid sample line in a direction to eliminate said difference andselecting b₁₅ and D₁₅ to minimize the flow through said sample line forsatisfying said equations.
 3. A method of taking a flowing sample of gasflowing through a line, which flowing sample is constantly proportionateto the flow rate of said flowing gas, said method comprising:a) passingsaid gas flowing through said line through a first flow restriction insaid line; b) drawing a flowing sample of said gas from said line at apoint upstream of said first flow restriction into a sample line; c)passing said flowing sample of said gas in said sample line through asecond flow restriction in said sample line, the interior of said line,said first flow restriction, said sample line, and said second flowrestriction each being substantially cylindrical, the interior diameterof each of said four elements above being sequentially identified by thefollowing symbols D₁₅, d₁₅, D₁₂ and d₁₂ ; d) equalizing the pressuredownstream of said first and second restrictions; and e) said first andsaid second flow restrictions being so sized with respect to each otherand said line and sample line that the equation F(b₁₅)+530/(D₁₅)^(1/2)=F(b₁₂)+530/(D₁₂)^(1/2) is true in the case of flange taps adjacent saidrestrictions when D₁₂ and D₁₅ are expressed in inches, and the equationF(b₁₅)+875/D₁₅ =F(b₁₂)+875/D₁₂ is true in the case of pipe taps adjacentsaid restrictions when D₁₂ and D₁₅ are expressed in inches, b₁₅ is aparameter of said second flow equal to the dimensionless quotientproduced by having d₁₅ divided by D₁₅, b₁₂ is equal to the dimensionlessquotient produced by having d₁₂ divided by D₁₂, F(b₁₅)=d₁₅ (830-5,000b₁₅ +9,000 b₁₅ ² -4200 b₁₅ ³ +B₁₅) wherein ##EQU63## for flange taps##EQU64## for pipe taps F(b₁₂)=d₁₂ (830-5000 b₁₂ +9000 b₁₂ ² -4200 b₁₂ ³+B₁₂) wherein ##EQU65## for flange taps ##EQU66## for pipe taps.
 4. Amethod in accordance with claim 3 in which said equalizing of downstreampressures is achieved by detecting the difference between said pressuresand operating a valve in said sample line in a direction to eliminatesaid difference and selecting b₁₅ and D₁₅ to minimize the flow throughsaid sample line for satisfying said equations.